(permutationsnil 3410114275"" (skosimp*)"" (expand "permutation_of?" )"" (inst 1 "(LAMBDA ii: ii)" )"" (expand "bijective?" )"" (prop)"1" (expand "injective?" ) (("1" (skosimp*) nil nil )) nil )"2" (expand "surjective?" )"2" (skosimp*)"2" (typepred "y!1" ) (("2" (inst + "y!1" ) nil nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil )"bool" permutations nil )"bool" functions nil )"bool" functions nil )NOT const-decl "[bool -> bool]" booleans nil )"bool" functions nil )nil nat_types nil )nil naturalnumbers nil )"nat" permutations nil )"bool" reals nil )nil naturalnumbers nil )"bool" reals nil )nil booleans nil )nil integers nil )"[rational -> boolean]" integers nil )nil rationals nil )"[real -> boolean]" rationals nil )nil reals nil )"[number_field -> boolean]" reals nil )nil number_fields nil )"[number -> boolean]" number_fieldsnil )nil booleans nil )nil numbers nil ))nil ))nil 3410114275"" (skosimp*)"" (expand "permutation_of?" )"" (skosimp*)"" (case-replace "N = 0" )"1" (inst + "f!1" )"1" (prop)"1" (skosimp*)"1" (inst?) (("1" (assert ) nil nil )) nil )) nil ))nil ))nil )"2" (inst + "inverse(f!1)" )"1" (rewrite "bij_inv_is_bij" )"1" (assert )"1" (skosimp*)"1" (inst -2 "inverse(f!1)(ii!1)" )"1" "f!1(inverse(f!1)(ii!1)) = ii!1" )"1" (assert ) nil nil )"2" (hide -2 2)"2" (expand "bijective?" )"2" (flatten)"2" "surjective_inverse[below[N],below[N]]" )"1" "inverse(f!1)(ii!1)" "ii!1" "f!1" )"1" (assert ) nil nil )"2" (inst 1 "0" ) nil nil ))nil )"2" (inst 1 "0" ) nil nil ))nil ))nil ))nil ))nil )"3" (inst 1 "0" ) nil nil ))nil )"2" (inst 1 "0" ) nil nil ))nil ))nil ))nil )"2" (inst 1 "0" ) nil nil ))nil )"2" (assert ) (("2" (inst 1 "0" ) nil nil )) nil ))nil ))nil ))nil ))nil ))nil )"bool" permutations nil )nil numbers nil )nil booleans nil )"[T, T -> boolean]" equalities nil )"[number -> boolean]" number_fieldsnil )nil number_fields nil )"[number_field -> boolean]" reals nil )nil reals nil )"[real -> boolean]" rationals nil )nil rationals nil )"[rational -> boolean]" integers nil )nil integers nil )nil booleans nil )"bool" reals nil )nil naturalnumbers nil )"nat" permutations nil )nil nat_types nil )nil naturalnumbers nil )"bool" reals nil )nil function_inverse nil )"bool" functions nil )nil function_inverse nil )"(strict_total_order?[real])" real_props nil )"[below(N) -> below(N)]" permutations nil )"bool" functions nil )"D" function_inverse nil )"bool" booleans nil ))nil ))nil 3410114275"" (skosimp*)"" (expand "permutation_of?" )"" (skosimp*)"" (inst 1 "(LAMBDA ii: f!2(f!1(ii)))" )"" (prop)"1" (expand "bijective?" )"1" (prop)"1" (expand "injective?" )"1" (skosimp*)"1" (inst -5 "f!1(x1!1)" "f!1(x2!1)" )"1" (inst -2 "x1!1" "x2!1" )"1" (assert ) nil nil )) nil ))nil ))nil ))nil )"2" (expand "surjective?" )"2" (skosimp*)"2" (inst -5 "y!1" )"2" (skosimp*)"2" (replace -5 * rl)"2" (inst -2 "x!1" )"2" (skosimp*)"2" "x!2" )"2" (assert ) nil nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil )"2" (skosimp*)"2" (inst?)"2" (inst?) (("2" (assert ) nil nil )) nil )) nil ))nil ))nil ))nil ))nil ))nil ))nil )"bool" permutations nil )nil numbers nil )nil booleans nil )"[number -> boolean]" number_fieldsnil )nil number_fields nil )"[number_field -> boolean]" reals nil )nil reals nil )"[real -> boolean]" rationals nil )nil rationals nil )"[rational -> boolean]" integers nil )nil integers nil )nil booleans nil )"bool" reals nil )nil naturalnumbers nil )"bool" reals nil )"nat" permutations nil )nil naturalnumbers nil )nil nat_types nil )"bool" functions nil )"bool" functions nil )"bool" functions nil ))nil ))nil 3410114275"" (skosimp*)"" (iff 1)"" (prop)"1" (expand "in?" )"1" (skosimp*)"1" (expand "permutation_of?" )"1" (skosimp*)"1" (inst 1 "f!1(ii!1)" )"1" (assert )"1" (inst?) (("1" (assert ) nil nil )) nil )) nil ))nil ))nil ))nil ))nil ))nil )"2" (expand "in?" )"2" (skosimp*)"2" (lemma "perm_symmetric" )"2" (inst -1 "A1!1" "A2!1" )"2" (assert )"2" (hide -3)"2" (expand "permutation_of?" )"2" (skosimp*)"2" (inst - "ii!1" )"2" (inst 1 "f!1(ii!1)" )"2" (assert ) nil nil )) nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil )nil permutations nil )nil permutations nil )"bool" below_arrays nil )"bool" permutations nil )nil numbers nil )nil booleans nil )"[number -> boolean]" number_fieldsnil )nil number_fields nil )"[number_field -> boolean]" reals nil )nil reals nil )"[real -> boolean]" rationals nil )nil rationals nil )"[rational -> boolean]" integers nil )nil integers nil )nil booleans nil )"bool" reals nil )nil naturalnumbers nil )"bool" reals nil )"nat" permutations nil )nil naturalnumbers nil )nil nat_types nil ))nil )))quality 100%
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